Finite Group Databasebeta

← #49121787

Subgroups — #49121787

Order 36224.

344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827231C211yesmaximal, characteristic, complemented
2#31827034C211yesmaximal, characteristic
3#31826471C211yesmaximal, characteristic, complemented
4#31826469C211yesmaximal, characteristic, complemented
5#31826438C211yesmaximal, characteristic, complemented
6#31826221C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C22×D1132C2211yescharacteristic
10#22583618—22no—
11#22583616—22no—
12C2×#17985376C2211yescharacteristic
13M16×D283—22no—
14#22583607C412yescomplemented
15#22583598C412yescomplemented
16#22583585—22no—
17#22583580—22no—
18#22583569C2211yescharacteristic
19#22583532—22no—
20#22583530—22no—
21#22583524—22no—
22C2×M16×C283C2211yescharacteristic
23#117×C283C2211yescharacteristic
24#117×C283C2211yescharacteristic
25C23×D283—21no—
26#17985392—21no—
27#17985392—21no—
28#17985392—21no—
29#17985392—21no—
30C2×Dic566C2×C411yescharacteristic
31C2×D1132—24no—
32C2×D1132—21no—
33C2×D1132—21no—
34C2×D1132—21no—
35C2×D1132—21no—
36C2×D1132—21no—
37C2×D1132C2×C412yes—
38C2×D1132C2×C411yescharacteristic
39C2×C22⋊D283D412yes—
40C2×C4×D283D412yes—
41#17985376—21no—
42#17985376—21no—
43#17985375—24no—
44C2×C283⋊C8D412yescomplemented
45C8×D283—24no—
46C4⋊Dic283—21no—
47C22⋊Dic283—21no—
48(C2×D283)⋊C4—24no—
49C4×Dic283—21no—
50C22×C4×C283C2311yescharacteristic
51M16×C283—21no—
52M16×C283—21no—
53C2×C8×C283D412yescomplemented
54C4⋊C4×C283—21no—
55C4⋊C4×C283—21no—
56C22⋊C4×C283—21no—
57C22⋊C4×C283—21no—
58C42×C283—21no—
59C42×C283C2×C412yes—
60C22×D283—22no—
61C22×D283—41no—
62C22×D283—41no—
63C22×D283—82no—
64C22×D283C22⋊C412yes—
65Dic566—21no—
66Dic566—21no—
67D1132—21no—
68D1132—21no—
69D1132—22no—
70D1132—22no—
71D1132—41no—
72D1132—41no—
73D1132—84no—
74C22⋊D283—22no—
75C22⋊D283—22no—
76C2×Dic283—41no—
77C2×Dic283C22⋊C412yes—
78C4×D283—22no—
79C4×D283—22no—
80C283⋊C8—22no—
81C23×C283C2×D411yescharacteristic
82C2×C4×C283—22no—
83C2×C4×C283—41no—
84C2×C4×C283C22×C411yescharacteristic
85C2×C4×C283C2×D411yescharacteristic
86C2×C4×C283C2×D411yescharacteristic
87C2×C4×C283C2×D411yescharacteristic
88C2×C4×C283#4111yescharacteristic
89C2×C4×C283#4111yescharacteristic
90C8×C283—22no—
91C22×C283—41no—
92C22×C283C2×C22⋊C411yescharacteristic
93C22×C283#12111yescharacteristic
94C22×C283#12111yescharacteristic
95C2×D283—22no—
96C2×D283—42no—
97C2×D283—44no—
98C2×D283—42no—
99C2×D283—82no—
100C2×D283—82no—
101C4×C283—42no—
102C4×C283—81no—
103C4×C283C4×D411yescharacteristic
104C4×C283C4×D411yescharacteristic
105C4×C283#12011yescharacteristic
106C4×C283#12311yescharacteristic
107Dic283—22no—
108Dic283—81no—
109C2×C283—21no—
110C2×C283—21no—
111C2×C283—21no—
112C2×C283#38611yescharacteristic
113D283—42no—
114D283—82no—
115C283#191011yescharacteristic, complemented, Sylow
116#1910—2831nomaximal, Sylow
117#568—2831no—
118#535—2831no—
119#418—2831no—
120#418—2831no—
121#410—2831no—
122H(3,ℤ/4)—2831no—
123H(3,ℤ/4)D28311yescharacteristic, complemented
124C2×#41—2831no—
125C22×D4—2831no—
126#131—5662no—
127#131—5662no—
128C2×M16—2831no—
129C2×M16—5662no—
130C2×M16C2×D28311yescharacteristic
131#127—2832no—
132#124—2832no—
133#121—5662no—
134#120—5662no—
135#117—2831no—
136#117C2×D28311yescharacteristic
137#117C2×D28311yescharacteristic
138#102—5662no—
139#102—5662no—
140#99—5662no—
141C24—5661no—
142#41—5661no—
143#41—5661no—
144#41—5661no—
145#41—5661no—
146C2×Q8—2831no—
147C2×D4—2832no—
148C2×D4—2831no—
149C2×D4—2832no—
150C2×D4—5664no—
151C2×D4—5661no—
152C2×D4—5661no—
153C2×D4—5661no—
154C2×D4—5661no—
155C2×D4—5661no—
156C22×C4—2832no—
157C22×C4C22×D28311yescharacteristic
158M16—21no—
159M16—21no—
160M16—5664no—
161M16—5661no—
162M16—5661no—
163C2×C8—2832no—
164C2×C8—5664no—
165C2×C8D113212yescomplemented
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—5661no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—5664no—
172C22⋊C4—5661no—
173C42—21no—
174C42—5661no—
175C42C4×D28312yes—
176C23—2832no—
177C23—5662no—
178C23—11321no—
179C23—11321no—
180C23—22642no—
181C23D4×D28311yescharacteristic
182Q8—5661no—
183Q8—5661no—
184D4—5662no—
185D4—5662no—
186D4—5661no—
187D4—5662no—
188D4—5661no—
189D4—5662no—
190D4—11321no—
191D4—11321no—
192D4—22644no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—2832no—
196C2×C4—5662no—
197C2×C4—5662no—
198C2×C4—11321no—
199C2×C4C2×C4×D28311yescharacteristic
200C2×C4D4×D28311yescharacteristic
201C2×C4D4×D28311yescharacteristic
202C2×C4C2×D113211yescharacteristic
203C2×C4#1798539211yescharacteristic
204C2×C4#1798539311yescharacteristic
205C8—22no—
206C8—5662no—
207C22—41no—
208C22—5662no—
209C22—11322no—
210C22—11324no—
211C22—11322no—
212C22—22642no—
213C22—22642no—
214C22C22⋊C4×D28311yescharacteristic
215C22#2258358311yescharacteristic
216C22#2258358511yescharacteristic
217C4—42no—
218C4—81no—
219C4—5662no—
220C4—22641no—
221C4#2258357211yescharacteristic
222C4C4×D113211yescharacteristic
223C4#2258358011yescharacteristic
224C4#2258359511yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—11322no—
229C2—22642no—
230C2#3182634311yescharacteristic
subgroupG/H
centerC2#31826343
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingH(3,ℤ/4)×C283C2
socleC2×C283#386
prime radical#31827034C2
cosocleC22×C4×C283C23
hypercenterH(3,ℤ/4)D283
hypocenterC283#1910
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #31827231C2semidirect
3. #31826471C2semidirect
4. #31826469C2semidirect
5. #31826438C2semidirect
6. #31826221C2semidirect
7. H(3,ℤ/4)×C283C2semidirect
14. #22583607C4semidirect
15. #22583598C4semidirect
44. C2×C283⋊C8D4semidirect
53. C2×C8×C283D4semidirect
115. C283#1910semidirect
123. H(3,ℤ/4)D283semidirect
165. C2×C8D1132semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#318272312
#318270342
#318264712
#318264692
#318264382
#318262212
H(3,ℤ/4)×C2832
#1910283